WARD {easyCODA}

Ward clustering of a compositional data matrix

Description

This function clusters the rows (or the columns, if the matrix is transformed) of a compositional data matrix, using weighted Ward clustering of the logratios.

Usage

WARD(LRdata, weight=TRUE, row.wt=NA)

Arguments

LRdata

Matrix of logratios, either a vector or preferably the logratio object resulting from one of the functions ALR, CLR, PLR or LR (usually CLRs will be used))

weight

TRUE (default) for weighted analysis (in which case weights are in the logratio object), FALSE for unweighted analysis, or a vector of user-defined column weights

row.wt

Optional set of row weights (default is equal weights when row.wt=NA)

Details

The function WARD performs a weighted WARD hierarchical clustering on the rows of an input set of logratios, usually CLR-transformed. (This would be equivalent to performing the clustering on all pairwise logratios). If the columns of the logratio matrix are unweighted, specify the option weight=FALSE: they will then get equal weights. The default weight=TRUE option implies that column weights are provided, either in the input list object LRdata, as LRdata$LR.wt, or as a vector of user-specified weights using the same weight option.

Value

An object which describes the tree produced by the clustering process on the n objects. The object is a list with components:

merge

an n-1 by 2 matrix. Row i of merge describes the merging of clusters at step i of the clustering. If an element j in the row is negative, then observation -j was merged at this stage. If j is positive then the merge was with the cluster formed at the (earlier) stage j of the algorithm. Thus negative entries in merge indicate agglomerations of singletons, and positive entries indicate agglomerations of non-singletons.

height

a set of n-1 real values (non-decreasing for ultrametric trees). The clustering height: that is, the value of the criterion associated with the clustering method for the particular agglomeration.

order

a vector giving the permutation of the original observations suitable for plotting, in the sense that a cluster plot using this ordering and matrix merge will not have crossings of the branches

Author(s)

Michael Greenacre

References

Greenacre, M. (2018), Compositional Data Analysis in Practice, Chapman & Hall / CRC.

See Also

hclust, CLR, LR.VAR, CLOSE

Examples

# clustering steps for unweighted and weighted logratios
# for both row- and column-clustering
data(cups)
cups <- CLOSE(cups)

# unweighted logratios: clustering samples
cups.uclr  <- CLR(cups, weight=FALSE)
cups.uward <- WARD(cups.uclr, weight=FALSE)   # weight=FALSE not needed here,
                                              # as equal weights are in object
plot(cups.uward)
# add up the heights of the nodes
sum(cups.uward$height)
# [1] 0.02100676
# check against the total logratio variance
LR.VAR(cups.uclr, weight=FALSE)
# [1] 0.02100676

# unweighted logratios: clustering parts
tcups <- t(cups)
tcups.uclr  <- CLR(tcups, weight=FALSE)
tcups.uward <- WARD(tcups.uclr, weight=FALSE)  # weight=FALSE not needed here,
                                               # as equal weights are in object
plot(tcups.uward, labels=colnames(cups))
sum(tcups.uward$height)
# [1] 0.02100676
LR.VAR(tcups.uclr, weight=FALSE)
# [1] 0.02100676

# weighted logratios: clustering samples
cups.clr <- CLR(cups)
cups.ward <- WARD(cups.clr)
plot(cups.ward)
sum(cups.ward$height)
# [1] 0.002339335
LR.VAR(cups.clr)
# [1] 0.002339335

# weighted logratios: clustering parts
# weight=FALSE is needed here, since we want equal weights
# for the samples (columns of tcups)
tcups.clr  <- CLR(tcups, weight=FALSE)
tcups.ward <- WARD(tcups.clr, row.wt=colMeans(cups))
plot(tcups.ward, labels=colnames(cups))
   sum(tcups.ward$height)
# [1] 0.002339335
LR.VAR(tcups.clr, row.wt=colMeans(cups))
# [1] 0.002339335